Solution of System of Linear Equation Using Matrix
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Matrix and Determinant

78953 If \(A\) is a square matrix of order 3 and \(|A|=5\), then \(\mid \mathbf{A}\) adj \(\mathbf{A} \mid\) is

1 125
2 25
3 625
4 5
Karnataka CET-2020
Matrix and Determinant

78954 The inverse of the matrix \(\left[\begin{array}{ccc}2 & 5 & 0 \\ 0 & 1 & 1 \\ -1 & 0 & 3\end{array}\right]\) is

1 \(\left[\begin{array}{ccc}3 & -1 & 1 \\ -15 & 6 & -5 \\ 5 & -2 & 2\end{array}\right]\)
2 \(\left[\begin{array}{ccc}3 & -15 & 5 \\ -1 & 6 & -2 \\ 1 & -5 & 2\end{array}\right]\)
3 \(\left[\begin{array}{ccc}3 & -5 & 5 \\ -1 & -6 & -2 \\ 1 & -5 & 2\end{array}\right]\)
4 \(\left[\begin{array}{ccc}3 & -15 & 5 \\ -1 & 6 & -2 \\ 1 & -5 & -2\end{array}\right]\)
Karnataka CET-2019
Matrix and Determinant

78955 If \(A=\left[\begin{array}{cc}\cos 2 \theta & -\sin 2 \theta \\ \sin 2 \theta & \cos 2 \theta\end{array}\right]\) and \(A+A^{T}=I\), where \(I\) is the unit matrix of \(2 \times 2 \& A^{T}\) is the transpose of \(A\), then the value of \(\theta\) is equal to

1 \(\frac{\pi}{6}\)
2 \(\frac{\pi}{3}\)
3 \(\pi\)
4 \(\frac{3 \pi}{2}\)
Karnataka CET-2016
Matrix and Determinant

78956 The inverse of the matrix \(A=\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4\end{array}\right]\) is

1 \(\frac{1}{24}\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4\end{array}\right]\)
2 \(\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4\end{array}\right]\)
3 \(\frac{1}{24}\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]\)
4 \(\left[\begin{array}{ccc}\frac{1}{2} & 0 & 0 \\ 0 & \frac{1}{3} & 0 \\ 0 & 0 & \frac{1}{4}\end{array}\right]\)
Karnataka CET-2014
Matrix and Determinant

78957 If \(A\) is a matrix of order 3 , such that \(A(\operatorname{adj} A)\) \(=10 \mathrm{I}\), then \(|\operatorname{adj} \mathbf{A}|=\)

1 1
2 10
3 100
4 \(10 \mathrm{I}\)
Karnataka CET-2014
NEET DIGITAL LIBRARY
Matrix and Determinant

78953 If \(A\) is a square matrix of order 3 and \(|A|=5\), then \(\mid \mathbf{A}\) adj \(\mathbf{A} \mid\) is

1 125
2 25
3 625
4 5
Karnataka CET-2020
Matrix and Determinant

78954 The inverse of the matrix \(\left[\begin{array}{ccc}2 & 5 & 0 \\ 0 & 1 & 1 \\ -1 & 0 & 3\end{array}\right]\) is

1 \(\left[\begin{array}{ccc}3 & -1 & 1 \\ -15 & 6 & -5 \\ 5 & -2 & 2\end{array}\right]\)
2 \(\left[\begin{array}{ccc}3 & -15 & 5 \\ -1 & 6 & -2 \\ 1 & -5 & 2\end{array}\right]\)
3 \(\left[\begin{array}{ccc}3 & -5 & 5 \\ -1 & -6 & -2 \\ 1 & -5 & 2\end{array}\right]\)
4 \(\left[\begin{array}{ccc}3 & -15 & 5 \\ -1 & 6 & -2 \\ 1 & -5 & -2\end{array}\right]\)
Karnataka CET-2019
Matrix and Determinant

78955 If \(A=\left[\begin{array}{cc}\cos 2 \theta & -\sin 2 \theta \\ \sin 2 \theta & \cos 2 \theta\end{array}\right]\) and \(A+A^{T}=I\), where \(I\) is the unit matrix of \(2 \times 2 \& A^{T}\) is the transpose of \(A\), then the value of \(\theta\) is equal to

1 \(\frac{\pi}{6}\)
2 \(\frac{\pi}{3}\)
3 \(\pi\)
4 \(\frac{3 \pi}{2}\)
Karnataka CET-2016
Matrix and Determinant

78956 The inverse of the matrix \(A=\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4\end{array}\right]\) is

1 \(\frac{1}{24}\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4\end{array}\right]\)
2 \(\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4\end{array}\right]\)
3 \(\frac{1}{24}\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]\)
4 \(\left[\begin{array}{ccc}\frac{1}{2} & 0 & 0 \\ 0 & \frac{1}{3} & 0 \\ 0 & 0 & \frac{1}{4}\end{array}\right]\)
Karnataka CET-2014
Matrix and Determinant

78957 If \(A\) is a matrix of order 3 , such that \(A(\operatorname{adj} A)\) \(=10 \mathrm{I}\), then \(|\operatorname{adj} \mathbf{A}|=\)

1 1
2 10
3 100
4 \(10 \mathrm{I}\)
Karnataka CET-2014
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Matrix and Determinant

78953 If \(A\) is a square matrix of order 3 and \(|A|=5\), then \(\mid \mathbf{A}\) adj \(\mathbf{A} \mid\) is

1 125
2 25
3 625
4 5
Karnataka CET-2020
Matrix and Determinant

78954 The inverse of the matrix \(\left[\begin{array}{ccc}2 & 5 & 0 \\ 0 & 1 & 1 \\ -1 & 0 & 3\end{array}\right]\) is

1 \(\left[\begin{array}{ccc}3 & -1 & 1 \\ -15 & 6 & -5 \\ 5 & -2 & 2\end{array}\right]\)
2 \(\left[\begin{array}{ccc}3 & -15 & 5 \\ -1 & 6 & -2 \\ 1 & -5 & 2\end{array}\right]\)
3 \(\left[\begin{array}{ccc}3 & -5 & 5 \\ -1 & -6 & -2 \\ 1 & -5 & 2\end{array}\right]\)
4 \(\left[\begin{array}{ccc}3 & -15 & 5 \\ -1 & 6 & -2 \\ 1 & -5 & -2\end{array}\right]\)
Karnataka CET-2019
Matrix and Determinant

78955 If \(A=\left[\begin{array}{cc}\cos 2 \theta & -\sin 2 \theta \\ \sin 2 \theta & \cos 2 \theta\end{array}\right]\) and \(A+A^{T}=I\), where \(I\) is the unit matrix of \(2 \times 2 \& A^{T}\) is the transpose of \(A\), then the value of \(\theta\) is equal to

1 \(\frac{\pi}{6}\)
2 \(\frac{\pi}{3}\)
3 \(\pi\)
4 \(\frac{3 \pi}{2}\)
Karnataka CET-2016
Matrix and Determinant

78956 The inverse of the matrix \(A=\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4\end{array}\right]\) is

1 \(\frac{1}{24}\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4\end{array}\right]\)
2 \(\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4\end{array}\right]\)
3 \(\frac{1}{24}\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]\)
4 \(\left[\begin{array}{ccc}\frac{1}{2} & 0 & 0 \\ 0 & \frac{1}{3} & 0 \\ 0 & 0 & \frac{1}{4}\end{array}\right]\)
Karnataka CET-2014
Matrix and Determinant

78957 If \(A\) is a matrix of order 3 , such that \(A(\operatorname{adj} A)\) \(=10 \mathrm{I}\), then \(|\operatorname{adj} \mathbf{A}|=\)

1 1
2 10
3 100
4 \(10 \mathrm{I}\)
Karnataka CET-2014
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Matrix and Determinant

78953 If \(A\) is a square matrix of order 3 and \(|A|=5\), then \(\mid \mathbf{A}\) adj \(\mathbf{A} \mid\) is

1 125
2 25
3 625
4 5
Karnataka CET-2020
Matrix and Determinant

78954 The inverse of the matrix \(\left[\begin{array}{ccc}2 & 5 & 0 \\ 0 & 1 & 1 \\ -1 & 0 & 3\end{array}\right]\) is

1 \(\left[\begin{array}{ccc}3 & -1 & 1 \\ -15 & 6 & -5 \\ 5 & -2 & 2\end{array}\right]\)
2 \(\left[\begin{array}{ccc}3 & -15 & 5 \\ -1 & 6 & -2 \\ 1 & -5 & 2\end{array}\right]\)
3 \(\left[\begin{array}{ccc}3 & -5 & 5 \\ -1 & -6 & -2 \\ 1 & -5 & 2\end{array}\right]\)
4 \(\left[\begin{array}{ccc}3 & -15 & 5 \\ -1 & 6 & -2 \\ 1 & -5 & -2\end{array}\right]\)
Karnataka CET-2019
Matrix and Determinant

78955 If \(A=\left[\begin{array}{cc}\cos 2 \theta & -\sin 2 \theta \\ \sin 2 \theta & \cos 2 \theta\end{array}\right]\) and \(A+A^{T}=I\), where \(I\) is the unit matrix of \(2 \times 2 \& A^{T}\) is the transpose of \(A\), then the value of \(\theta\) is equal to

1 \(\frac{\pi}{6}\)
2 \(\frac{\pi}{3}\)
3 \(\pi\)
4 \(\frac{3 \pi}{2}\)
Karnataka CET-2016
Matrix and Determinant

78956 The inverse of the matrix \(A=\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4\end{array}\right]\) is

1 \(\frac{1}{24}\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4\end{array}\right]\)
2 \(\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4\end{array}\right]\)
3 \(\frac{1}{24}\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]\)
4 \(\left[\begin{array}{ccc}\frac{1}{2} & 0 & 0 \\ 0 & \frac{1}{3} & 0 \\ 0 & 0 & \frac{1}{4}\end{array}\right]\)
Karnataka CET-2014
Matrix and Determinant

78957 If \(A\) is a matrix of order 3 , such that \(A(\operatorname{adj} A)\) \(=10 \mathrm{I}\), then \(|\operatorname{adj} \mathbf{A}|=\)

1 1
2 10
3 100
4 \(10 \mathrm{I}\)
Karnataka CET-2014
NEET DIGITAL LIBRARY
Matrix and Determinant

78953 If \(A\) is a square matrix of order 3 and \(|A|=5\), then \(\mid \mathbf{A}\) adj \(\mathbf{A} \mid\) is

1 125
2 25
3 625
4 5
Karnataka CET-2020
Matrix and Determinant

78954 The inverse of the matrix \(\left[\begin{array}{ccc}2 & 5 & 0 \\ 0 & 1 & 1 \\ -1 & 0 & 3\end{array}\right]\) is

1 \(\left[\begin{array}{ccc}3 & -1 & 1 \\ -15 & 6 & -5 \\ 5 & -2 & 2\end{array}\right]\)
2 \(\left[\begin{array}{ccc}3 & -15 & 5 \\ -1 & 6 & -2 \\ 1 & -5 & 2\end{array}\right]\)
3 \(\left[\begin{array}{ccc}3 & -5 & 5 \\ -1 & -6 & -2 \\ 1 & -5 & 2\end{array}\right]\)
4 \(\left[\begin{array}{ccc}3 & -15 & 5 \\ -1 & 6 & -2 \\ 1 & -5 & -2\end{array}\right]\)
Karnataka CET-2019
Matrix and Determinant

78955 If \(A=\left[\begin{array}{cc}\cos 2 \theta & -\sin 2 \theta \\ \sin 2 \theta & \cos 2 \theta\end{array}\right]\) and \(A+A^{T}=I\), where \(I\) is the unit matrix of \(2 \times 2 \& A^{T}\) is the transpose of \(A\), then the value of \(\theta\) is equal to

1 \(\frac{\pi}{6}\)
2 \(\frac{\pi}{3}\)
3 \(\pi\)
4 \(\frac{3 \pi}{2}\)
Karnataka CET-2016
Matrix and Determinant

78956 The inverse of the matrix \(A=\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4\end{array}\right]\) is

1 \(\frac{1}{24}\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4\end{array}\right]\)
2 \(\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4\end{array}\right]\)
3 \(\frac{1}{24}\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]\)
4 \(\left[\begin{array}{ccc}\frac{1}{2} & 0 & 0 \\ 0 & \frac{1}{3} & 0 \\ 0 & 0 & \frac{1}{4}\end{array}\right]\)
Karnataka CET-2014
Matrix and Determinant

78957 If \(A\) is a matrix of order 3 , such that \(A(\operatorname{adj} A)\) \(=10 \mathrm{I}\), then \(|\operatorname{adj} \mathbf{A}|=\)

1 1
2 10
3 100
4 \(10 \mathrm{I}\)
Karnataka CET-2014